For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The diffraction limit originates from the Heisenberg uncertainty principle. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available. Recent work on band-limited functions oscillating faster than the highest Fourier components of which they are composed, so termed superoscillations, shows that there may be routes to sub-diffraction imaging in the optical far-field without the need to retain rapidly decaying evanescent waves. With superoscillations, however, sub-diffraction features are achieved at the expense of having most of the energy in low frequency Fourier features (side-bands) that have many orders of magnitude higher amplitude than any sub-diffractive feature that is to be utilized.